This paper extends to infinite graphs the most general extremal issues, which are problems of determining the maximumnumber of edges of a graph not containing a given subgraph. It also relates the new results with the corresponding situationsfor the finite case. In particular, concepts from ‘finite’ graph theory, like the average degree and the extremal number, aregeneralized and computed for some specific cases. Finally, some applications of infinite graphs to the transportation ofdangerous goods are presented; they involve the analysis of networks and percolation thresholds.
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